I know what you mean by hating online buying when you read so many news about hacked credit card data. Because of that, I never use credit card directly for online buying, but my Pay Pal account. I do use credit card in fact as it's linked to my pay pal acc but the card's data is not shown anywhere during the purchase process.
However you may use US bank account instead of credit card with Pay Pal. If that will satisfy you, register on www.paypal.com
Also there are some other methods of secure payment on steam, amazon etc, you may check those too (moneybookers, etc).
For Battlefield 3 I don't know how that works as I despise that type of games and would never buy it, sorry. Can you please describe the process from it a bit?
In some countries the major credit brands are now offering "Pre-paid credit cards" too. They're basically debit cards, but are formatted as credit cards. They will decline unless you have a positive balance and you only need to put money in them when you plan on making a purchase.